Beam propagation and shift-variant optics.

Abstract

The goal of the research described in this dissertation is to be able to model propagation of light through shift-variant optics. Shift-variant optical elements have a point spread function which is a function of the transverse coordinates. This shift-variance can be caused by aberration or by the first order properties of the optical system. In this work the latter is emphasized. Specifically, this dissertation discusses propagation through lenses and prisms and between tilted planes or a plane and a spherical surface. Extension to other types of shift-variant optical elements is possible. Two methods for performing the propagation are described. One, the beam division model, divides the beam into isoplanatic patches, separately propagates the patches and recombines them on the observation surface. The second method, the mapping model, maps the beam into a space in which the propagation is shift-invariant, propagates and then maps back into real space. Experimental verification of these methods is demonstrated by means of the Talbot effect. The setup consists of a collimated laser beam passing through a Ronchi ruling of about ten cycles per millimeter. With no intervening optics, Talbot images of the ruling are formed which are parallel to the wavefronts. When a prism at minimum deviation is placed in the outgoing beam, it causes the Talbot images to be tilted with respect to the wavefronts. If a stigmatic unit magnification telescope replaces the prism, the Talbot images are formed on surfaces congruent to the Petzval surface.